As I've seen posted elsewhere...if the push is in the centre of the pitch it's just a push. Not sure there's a rule where a push becomes more of a push given added dangers! I even think Firminho stopped his run forcing contact from behind.
The ref really did a poor job though...both players were worthy of a yellow card for everything that followed the push.
Re any racist comments made, we all know the whole issue will be swept under the carpet...can't have another slur on Merseyside. Different issue with a Manchester club being the victim...can't see 2 Liverpool clubs letting the city go through the fallout.